Details

sample308.0ms

Algorithm

intervals

Results

92.0ms	104×	body	1280	valid
45.0ms	41×	body	10240	exit
33.0ms	14×	body	320	nan
30.0ms	51×	body	640	valid
18.0ms	152×	body	80	valid
18.0ms	22×	body	1280	nan
16.0ms	36×	body	320	valid
15.0ms	167×	body	80	nan
12.0ms	20×	body	640	nan
4.0ms	15×	body	160	valid
1.0ms	3×	body	160	nan

simplify278.0ms

Counts

1 → 1

Calls

1 calls:

Slowest

278.0ms

(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.2b

localize20.0ms

Local error

Found 3 expressions with local error:

3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))
0.3b	(pow x (/ 1 n))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

76×	`*-un-lft-identity`
73×	`unpow-prod-down`
63×	`add-sqr-sqrt`
56×	`prod-diff`
51×	`add-cube-cbrt`
26×	`pow-unpow`
24×	`sqr-pow`
18×	`times-frac`
10×	`distribute-lft-out`
9×	`difference-of-squares`
8×	`fma-neg`
5×	`pow1` `add-exp-log` `add-log-exp`
3×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `distribute-lft-out--`
2×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

3 → 152

Calls

3 calls:

Slowest

63.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
12.0ms	(pow (+ x 1) (/ 1 n))
3.0ms	(pow x (/ 1 n))

series466.0ms

Counts

3 → 9

Calls

3 calls:

Slowest

246.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
145.0ms	(pow (+ x 1) (/ 1 n))
74.0ms	(pow x (/ 1 n))

simplify44.3s

Counts

188 → 161

Calls

188 calls:

Slowest

702.0ms	(fma (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ 1 n)) (pow 1 (/ 1 n)))))
677.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
615.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
590.0ms	(- (sqrt (pow (+ x 1) (/ 1 n))) (sqrt (pow x (/ 1 n))))
577.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (sqrt (pow x (/ 1 n))))

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.5b

localize38.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))
0.7b	(pow (+ x 1) (/ 1 n))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

39×	`pow-unpow`
34×	`*-un-lft-identity`
28×	`add-sqr-sqrt` `add-cube-cbrt`
27×	`times-frac`
12×	`unpow-prod-down`
7×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv` `distribute-lft-out` `sqr-pow`
1×	`fma-udef`

Counts

4 → 104

Calls

4 calls:

Slowest

7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
7.0ms	(pow (+ x 1) (/ 1 n))
0.0ms	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))

series1.1s

Counts

4 → 12

Calls

4 calls:

Slowest

803.0ms	(fma (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n))) (- (* (pow x (/ (/ 1 n) 2)) (pow x (/ (/ 1 n) 2)))))
112.0ms	(pow (+ x 1) (/ 1 n))
106.0ms	(pow (+ x 1) (/ 1 n))
105.0ms	(pow (+ x 1) (/ 1 n))

simplify3.6s

Counts

69 → 116

Calls

69 calls:

Slowest

387.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
387.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
337.0ms	(pow (* (cbrt (+ x 1)) (cbrt (+ x 1))) (/ 1 n))
271.0ms	(- (+ (/ (log -1) (* x (pow n 2))) (/ 1 (* x n))) (+ (* 1/2 (/ 1 (* (pow x 2) n))) (/ (log (/ -1 x)) (* x (pow n 2)))))
252.0ms	(- (+ (/ (log -1) n) (+ 1 (/ 1 (* x n)))) (/ (log (/ -1 x)) n))

prune2.3s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.4b

localize43.0ms

Local error

Found 4 expressions with local error:

3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))

rewrite312.0ms

Algorithm

rewrite-expression-head

Rules

202×	`unpow-prod-down`
179×	`*-un-lft-identity`
168×	`prod-diff`
144×	`add-sqr-sqrt`
108×	`add-cube-cbrt`
67×	`sqr-pow`
28×	`distribute-lft-out`
27×	`difference-of-squares`
24×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac` `distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 304

Calls

4 calls:

Slowest

112.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
101.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
83.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
10.0ms	(pow (+ x 1) (/ 1 n))

series879.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

289.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
259.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
224.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
106.0ms	(pow (+ x 1) (/ 1 n))

simplify2.1m

Counts

460 → 316

Calls

460 calls:

Slowest

857.0ms	(fma (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt (+ x 1)) (/ 1 n)) (- (* (pow x (/ 1 n)) 1)))
836.0ms	(fma (pow (+ x 1) (/ (/ 1 n) 2)) (pow (+ x 1) (/ (/ 1 n) 2)) (- (* (pow x (/ 1 n)) 1)))
697.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
679.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
672.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))

prune4.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.4b

localize70.0ms

Local error

Found 4 expressions with local error:

3.8b	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))
3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
3.3b	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
0.7b	(pow (+ x 1) (/ 1 n))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

139×	`unpow-prod-down`
126×	`*-un-lft-identity`
119×	`prod-diff`
102×	`add-sqr-sqrt`
78×	`add-cube-cbrt`
46×	`sqr-pow`
19×	`distribute-lft-out`
18×	`difference-of-squares`
17×	`fma-neg`
13×	`pow-unpow`
10×	`add-log-exp`
9×	`times-frac`
6×	`distribute-lft-out--`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u`
3×	`sub-neg` `flip3--` `diff-log` `flip--`
1×	`pow-to-exp` `pow-pow` `pow-exp` `div-inv`

Counts

4 → 236

Calls

4 calls:

Slowest

127.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))
111.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
82.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
13.0ms	(pow (+ x 1) (/ 1 n))

series795.0ms

Counts

4 → 12

Calls

4 calls:

Slowest

267.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
231.0ms	(- (* (* (cbrt (pow (+ x 1) (/ 1 n))) (cbrt (pow (+ x 1) (/ 1 n)))) (cbrt (pow (+ x 1) (/ 1 n)))) (pow x (/ 1 n)))
215.0ms	(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
81.0ms	(pow (+ x 1) (/ 1 n))

simplify1.5m

Counts

333 → 248

Calls

333 calls:

Slowest

914.0ms	(fma (pow 1 (/ 1 n)) (pow (+ x 1) (/ 1 n)) (- (* (pow (sqrt x) (/ 1 n)) (pow (sqrt x) (/ 1 n)))))
810.0ms	(fma 1 (pow (+ x 1) (/ 1 n)) (- (* (pow (cbrt x) (/ 1 n)) (pow (* (cbrt x) (cbrt x)) (/ 1 n)))))
741.0ms	(- (pow (+ x 1) (/ (/ 1 n) 2)) (pow (sqrt x) (/ 1 n)))
705.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))
678.0ms	(+ (pow (sqrt (+ x 1)) (/ 1 n)) (pow (sqrt x) (/ 1 n)))

prune4.3s

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 20.4b

regimes418.0ms

Accuracy

86.2% (1.6b remaining)

Error of 19.9b against oracle of 18.3b and baseline of 30.2b

bsearch1.2s

end0.0ms

sample9.5s

Algorithm

intervals

Results

3.3s	3240×	body	1280	valid
1.3s	1193×	body	10240	exit
1.1s	1606×	body	640	valid
971.0ms	4723×	body	80	valid
697.0ms	647×	body	1280	nan
567.0ms	5310×	body	80	nan
417.0ms	663×	body	640	nan
379.0ms	856×	body	320	valid
161.0ms	352×	body	320	nan
114.0ms	431×	body	160	valid
47.0ms	195×	body	160	nan